

A099480


Count from 1, repeating 2n five times.


4



1, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 7, 8, 8, 8, 8, 8, 9, 10, 10, 10, 10, 10, 11, 12, 12, 12, 12, 12, 13, 14, 14, 14, 14, 14, 15, 16, 16, 16, 16, 16, 17, 18, 18, 18, 18, 18, 19, 20, 20, 20, 20, 20, 21, 22, 22, 22, 22, 22, 23, 24, 24, 24, 24, 24, 25, 26, 26, 26, 26, 26
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OFFSET

0,2


COMMENTS

Could be called the Jones sequence of the knot 9_43, since the g.f. is the reciprocal of (a parameterization of) the Jones polynomial for 9_43.
Half the domination number of the knight's graph on a 2 X (n+1) chessboard.  David Nacin, May 28 2017


LINKS

Table of n, a(n) for n=0..77.
Index entries for linear recurrences with constant coefficients, signature (2,2,2,2,2,1).


FORMULA

G.f.: 1/((1x+x^2)(1xx^3+x^4)) = 1/(12x+2x^22x^3+2x^42x^5+x^6);
a(n) = 2*a(n1)2*a(n2)+2*a(n3)2*a(n4)+2*a(n5)a(n6), n>5;
a(n) = cos(Pi*2n/3+Pi/3)/6+sqrt(3)*sin(Pi*2n/3+Pi/3)/18sqrt(3)*cos(Pi*n/3+Pi/6)/6+sin(Pi*n/3+Pi/6)/2+(n+3)/3.
a(n) = Sum_{i=0..n+1} floor((i1)/6)  floor((i3)/6).  Wesley Ivan Hurt, Sep 08 2015
a(n) = A287393(n+1)/2.  David Nacin, May 28 2017


MATHEMATICA

LinearRecurrence[{2, 2, 2, 2, 2, 1}, {1, 2, 2, 2, 2, 2}, 100] (* Vincenzo Librandi, Sep 09 2'15 *)


PROG

(MAGMA) I:=[1, 2, 2, 2, 2, 2]; [n le 6 select I[n] else 2*Self(n1)2*Self(n2)+2*Self(n3)2*Self(n4)+2*Self(n5)Self(n6): n in [1..100]]; // Vincenzo Librandi, Sep 09 2015


CROSSREFS

Cf. A099479, A287393.
Sequence in context: A329097 A197054 A120502 * A025783 A025780 A199121
Adjacent sequences: A099477 A099478 A099479 * A099481 A099482 A099483


KEYWORD

easy,nonn


AUTHOR

Paul Barry, Oct 18 2004


STATUS

approved



